Question

a particle moves in a straight line with a constant acceleration it changes its velocity from 10m/s to 20m/s while passing through a distance 135m in t seconds the value of t is"

Answer 1

Hey there!

Given that a particle is moving in a straight line with a constant acceleration , and changes its velocity from 10m/s to 20 m/s while passing through a distance 135 m in t seconds, the value of t is ____

So,
Initial velocity ( u ) = 10 m/s

Final velocity ( v) = 20 m/s

Displacement ( s) = 135 m.


We know that ,

From the laws of equation ,

v² - u² = 2as

Substituting the values,

20² - 10² = 2( a) ( s)

400 -100 = 2 ( a) ( 135 )

300 = 270 a

a = 300/270

a = 10/9

Now, Use other laws of equation,

v = u + a t

20 = 10 + ( 10/9 ) t

10 = 10/9 * t

90/10 = t

t = 9 seconds.

Therefore, The time taken to change the velocity of 10 m/s to 20 m/s passing through a distance 135 m.

Answer 2

Given conditions ⇒

Initial velocity (u) = 10 m/s

Final velocity (v) = 20 m/s

Displacement(S) covered by the Object = 135 m.

Using the Third Equation of the Galileo's Equation,

v² - u² = 2aS

Substituting the values,

(20)² - (10)² = 2a(135)

⇒ 400 - 100 = 270a

∴ 270a = 300

⇒ a = 10/9 m/s².

Now, Using the Galileo's First Equation of Motion,

v - u = at

20 - 10 = 10/9 × t

10 = 10/9 × t

⇒ t = 9

Hence, the time taken by the Particles moving in a Straight line is 9 seconds.

Hope it helps.